Showing content from https://dlmf.nist.gov/4.31 below:
§4.31 Special Values and Limits ⣠Hyperbolic Functions ⣠Chapter 4 Elementary Functions
§4.31 Special Values and Limits â
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Keywords:
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hyperbolic functions, limits, special values
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Notes:
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See Hobson (1928, p. 326), Levinson and Redheffer (1970, p. 61).
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Permalink:
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http://dlmf.nist.gov/4.31
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Annotations for Ch.4
Table 4.31.1: Hyperbolic functions: values at multiples of 1 2 â¢ Ï â¢ i . z 0 1 2 â¢ Ï â¢ i Ï â¢ i 3 2 â¢ Ï â¢ i â sinh â¡ z 0 i 0 â i â cosh â¡ z 1 0 â 1 0 â tanh â¡ z 0 â ⢠i 0 â â ⢠i 1 csch â¡ z â â i â i 0 sech â¡ z 1 â â 1 â 0 coth â¡ z â 0 â 0 1 â
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Symbols:
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Ï : the ratio of the circumference of a circle to its diameter, csch â¡ z : hyperbolic cosecant function, cosh â¡ z : hyperbolic cosine function, coth â¡ z : hyperbolic cotangent function, sech â¡ z : hyperbolic secant function, sinh â¡ z : hyperbolic sine function, tanh â¡ z : hyperbolic tangent function, i : imaginary unit and z : complex variable
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A&S Ref:
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4.5.61
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http://dlmf.nist.gov/4.31.T1
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Annotations for §4.31 and Ch.4
4.31.1 lim z â 0 sinh â¡ z z = 1 , â
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Symbols:
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sinh â¡ z : hyperbolic sine function and z : complex variable
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http://dlmf.nist.gov/4.31.E1
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TeX, pMML, png
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Annotations for §4.31 and Ch.4
4.31.2 lim z â 0 tanh â¡ z z = 1 , â
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Symbols:
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tanh â¡ z : hyperbolic tangent function and z : complex variable
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Permalink:
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http://dlmf.nist.gov/4.31.E2
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Annotations for §4.31 and Ch.4
4.31.3 lim z â 0 cosh â¡ z â 1 z2 = 1 2 . â
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Symbols:
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cosh â¡ z : hyperbolic cosine function and z : complex variable
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Permalink:
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http://dlmf.nist.gov/4.31.E3
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Encodings:
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TeX, pMML, png
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See also:
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Annotations for §4.31 and Ch.4
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